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5
votes
1answer
132 views

Degree restriction for polynomials in $\mathsf{VP}$

why do we need the restriction on the degree for a polynomial to be in VP due to which $(\prod_{i=0}^{n} x_i)^{2^n}$ $\notin$ VP even though it has a poly-size circuit?
14
votes
0answers
191 views

Random functions of low degree as a real polynomial

Is there a (reasonable) way to sample a uniformly random boolean function $f:\{0,1\}^n \to \{0,1\}$ whose degree as a real polynomial is at most $d$? EDIT: Nisan and Szegedy have shown that a ...
12
votes
4answers
669 views

hardness of approximating the chromatic number in graphs with bounded degree

I am looking for hardness results on vertex coloring of graphs with bounded degree. Given a graph $G(V,E)$, we know that for any $\epsilon>0$, it's hard to approximate $\chi(G)$ within a factor ...
3
votes
1answer
149 views

bounded outdegree bipartite spanners

Given an undirected graph $G = (V,E)$ and an integer $k > 0$, our objective is to find a subgraph $G' = (V ,E')$ where $E' \subseteq E$ such that $G'$ has the three following properties : $G'$ ...
16
votes
2answers
494 views

Is feedback vertex set problem is solvable in polynomial time for 3-degree bounded graphs?

Feedback Vertex Set is NP-complete for general graphs. It is known to be NP-complete for degree-8 bounded graphs due to a reduction from vertex cover. The Wikipedia article says that it is poly-time ...
-1
votes
2answers
184 views

Complexity of finding if a degree bounded graph H is a subgraph of an unbounded graph G

You are given two graphs G and H , and want to know if H is a subgraph of G. You know that H has a max vertex degree K (constant integer). What can you say about the complexity of this? I know that ...
10
votes
1answer
258 views

Hardness of approximating fractional chromatic number on bounded degree graphs

Is it apx-hard to approximate fractional chromatic number on bounded degree graphs?